SOLUTION: express root of 48 in the form root of b where a is an integer

Algebra ->  Square-cubic-other-roots -> SOLUTION: express root of 48 in the form root of b where a is an integer       Log On


   

Question 857101: express root of 48 in the form root of b where a is an integer
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Simplifying Square Roots (whole numbers only)
sqrt%2848%29 Start with the given expression


The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.

So let's list the factors of 48

Factors:

1, 2, 3, 4, 6, 8, 12, 16, 24, 48



Notice how 16 is the largest perfect square, so lets factor 48 into 16*3





sqrt%2816%2A3%29 Factor 48 into 16*3



sqrt%2816%29%2Asqrt%283%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29



4%2Asqrt%283%29 Take the square root of the perfect square 16 to get 4



So the expression sqrt%2848%29 simplifies to 4%2Asqrt%283%29



----------------------------
Check:

Notice if we evaluate the square root of 48 with a calculator we get


sqrt%2848%29=6.92820323027551


and if we evaluate 4%2Asqrt%283%29 we get


4%2Asqrt%283%29=6.92820323027551


This shows that sqrt%2848%29=4%2Asqrt%283%29. So this verifies our answer